Syntax

Description

The procedure f := stats::weibullRandom(a, b) can
be called in the form f(). The return value of f() is
either a floating-point number or a symbolic expression:

If a and b can be converted
to positive floating-point numbers, then f() returns
a nonnegative floating-point number.

In all other cases, stats::weibullRandom(a, b)() is
returned symbolically.

Numerical values of a and b are
only accepted if they are real and positive.

The values X = f() are distributed randomly
according to the cumulative distribution function of the Weibull distribution
with parameters a and b. For
any 0 ≤ x,
the probability that X ≤ x is
given by .

Without the option Seed = s,
an initial seed is chosen internally. This initial seed is set to
a default value when MuPAD® is started. Thus, each time MuPAD is
started or re-initialized with the reset function, random generators produce
the same sequences of numbers.

Note:
In contrast to the function random, the generators produced by stats::weibullRandom do
not react to the environment variable SEED.

For efficiency, it is recommended to produce sequences of K random
numbers via

f := stats::weibullRandom(a, b): f() $k = 1..K;

rather than by

stats::weibullRandom(a, b)() $k = 1..K;

The latter call produces a sequence of generators each of which
is called once. Also note that

stats::weibullRandom(a, b, Seed = n)() $k = 1..K;

does not produce a random sequence, because a sequence of freshly
initialized generators would be created each of them producing the
same number.

Environment Interactions

The function is sensitive to the environment variable DIGITS which
determines the numerical working precision.

Examples

Example 1

We generate Weibull deviates with parameters a = 2 and b = :

f := stats::weibullRandom(2, 3/4): f() $ k = 1..4

delete f:

Example 2

With symbolic parameters, no random floating-point numbers can
be produced:

f := stats::weibullRandom(a, b): f()

When positive real numbers are assigned to a and b,
the function f starts to produce random floating
point numbers:

Parameters

Options

Seed

Option, specified as Seed = s

Initializes the random generator with the integer seed s. s can
also be the option CurrentTime, to make the seed
depend on the current time.

This option serves for generating generators that return predictable
sequences of pseudo-random numbers. The generator is initialized with
the seed s which may be an arbitrary integer. Several
generators with the same initial seed produce the same sequence of
numbers.

When this option is used, the parameters a and b must
be convertible to positive floating-point numbers at the time when
the random generator is generated.